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Triangle Bisectors
Many different terms for bisectors of triangles.
Term | Definition |
---|---|
Segment Bisector | Any segment, line, or plane that intersects a segment at its midpoint (Cuts a segment into 2 congruent line segments). |
Perpendicular Bisector | A segment bisector that is also perpendicular to the segment it is bisecting. |
Locus | A set of points that satisfies a particular condition. |
Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. |
Converse of the Perpendicular Bisector Theorem | If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |
Concurrent Lines | When 3 or more lines intersects at a common point. |
Point of Concurrency | The point where concurrent lines intersect. |
Circumcenter of a Triangle | The point of concurrency of the 3 perpendicular bisectors of a triangle. |
Circumcenter Theorem | The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. |
Angle Bisector | A line, segment, or ray that divides an angle into 2 congruent angles. |
Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. |
Converse of the Angle Bisector Theorem | If a point in the interior of an angle is equidistant from the sides of an angle, then it is on the bisector of the angle. |
Incenter of a Triangle | The point of concurrency of the 3 angle bisectors of a triangle. |
Incenter Theorem | The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle. |